Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology Tobias Otto: A short course on radar meteorology.1 A short course on

Remote Sensing of the Environment (RSE)

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AATTMMOOSS

DelftUniversity ofTechnology Tobias Otto: A short course on radar meteorology. 1

A short course on radar meteorology

Tobias Otto


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Radar Meteorology

Reference: AMS Glossary

Radar: Radio Detection And Ranging

An electronic instrument used for the detection and ranging of distant objects of such composition that they scatter or reflect radio energy.

Meteorology:

The study of the physics, chemistry, and dynamics of the Earth's atmosphere.

Radar Meteorology:

The study of the atmosphere and weather using radar as the means of observation and measurement.


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Microwaves

HF 3 - 30 MHzVHF 30 - 300 MHzUHF 300 - 1000 MHzL 1 - 2 GHzS 2 - 4 GHzC 4 - 8 GHzX 8 - 12 GHzKu 12 - 18 GHzK 18 - 27 GHzKa 27 - 40 GHzV 40 - 75 GHzW 75 - 110 GHzmm 110 - 300 GHz

KNMI Windprofiler

IDRA

Cloud Radar

WLAN

mobilephones

Reference: Radar-frequency band nomenclature (IEEE Std. 521-2002)

KNMIWeatherRadar

PARSAX


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T. Otto

electromagnetic waves

frequency ≈ 2.4 GHzwavelength ≈ 12 cm

scattering

absorption

Microwaves and Water


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PARSAX on top of EWI faculty

T. Otto

receivedpower

time

radar

Water and Radar


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Information in microwaves

1. Amplitudecan be related to the strength of precipitation / rain rate

Electromagnetic waves are transversal waves, i.e. their direction of oscillation is orthogonal to their direction of propagation.

AA

xy

z


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xy

z


2. FrequencyDoppler shift, relative radial velocity of the precipitation


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xy

z



3. Phasecan be used to measure refractive index variations

y


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x

y

z



3. Phasecan be used to measure refractive index variations

4. Polarisationhydrometeor / rain drop shape


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Radar Meteorology




Meteorology:


Radar Meteorology:



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Radar Equation for a Point Target

Pt

Pr

Gt

Gr

transmitter

receiver

antennae range R

targetσ

Pt .. transmitted power (W)Gt .. antenna gain on transmitR .. range (m)σ .. radar cross section (m2)Gr .. antenna gain on receivePr .. received power (W)

44

1

4

2

22r

tt

r

G

RG

R

PP

backscattered power densityat receiving antenna

isotropicantenna

power density incidenton the target

effective area ofthe receiving antenna


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Radar Equation for a Point Target

Pt

Pr

Gt

Gr

transmitter

receiver

antennae range R

targetσ

Pt .. transmitted power (W)Gt .. antenna gain on transmitR .. range (m)σ .. radar cross section (m2)Gr .. antenna gain on receivePr .. received power (W)

43

2

4

R

GGPP rttr

radar constant target characteristics

free-spacepropagation


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From Point to Volume Targets

- the radar equation for a point target needs to be customised and expandedto fit the needs of each radar application(e.g. moving target indication, synthetic aperture radar, and also meterological radar)

- radar has a limited spatial resolution, it does not observe single targets (i.e. raindrops, ice crystals etc.), instead it always measures a volume filled| with a lot of targets

volume (distributed) target instead of a point target

- to account for this, the radar cross section is replaced with the sum of theradar cross sections of all scatterers in the resolution volume V (range-bin):

eunit volumbinrange

ii V


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Radar Resolution Volume

range Rradar resolution volume

(range-bin) B

cr

2

c .. speed of lightB .. bandwidth of the transmitted signal

(the bandwith of a rectangular pulse is the inverse its duration B=1/τ)

Δr is typically between 3m - 300m,and the antenna beam-width is between 0.5° - 2° for weather radars

θ

antenna beam-width


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Range Resolution of a Pulse Radar


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e.g. pulse duration 1 µs300 m

1 2 3

mc )(s

f0


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1 2 3

target 1response

target 2response

target 3response

Now we samplethe backscattered signal.

2

c

• each sample consists of the sum of the backscattered signals of a volume withthe length c·τ/2

• for a pulse radar, the optimum sampling rate of the backscattered signal is 2/τ (Hz)


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Radar Equation for Volume Targets

2 2 2

3 4unit volume

16 ln 24t t r

r i

PGG R cP

BR

2

3 4unit volume

4t t r

r i

PGGP V

R

B

cr

2

R

θ/2

B

crV

22

r B

cRV

22tan

2

tan(α) ≈ α (rad) for small α

2ln2

1

24

rad 22

B

cRV

2

volume reduction factor due toGaussian antenna beam pattern


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Radar Cross Section σ

)m( 2

incident

redbackscatte

S

P

Pbackscattered

Sincident

.. backscattered power (W)

.. incident power density (W/m2)

Depends on:

- frequency and polarisation of the electromagnetic wave

- scattering geometry / angle- electromagnetic properties of

the scatterer- target shape

hydrometeors can be approximated as spheres


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Monostatic radar cross section of a conducting sphere:

a

.. radius of the sphere

.. wavelength

Rayleigh region: a <<

Resonance / Mie region:

Optical region: a >>

Figure: D. Pozar, “Microwave Engineering”, 2nd edition, Wiley.

norm

alis

ed r

adar

cro

ss s

ectio

n

electrical size


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hydrometeors are small compared to the wavelengths used in weather radar

observations: weather radar wavelength 9cm max. 6mm raindrop diameter

Rayleigh scattering approximation can be applied;

radar cross section for dielectric spheres:

4

625

ii

DK

D|K|2

.. hydrometeor diameter

.. wavelength

.. dielectric factor depending on the material of the scatterer


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Radar Equation for Weather Radar

eunit volum

64

2522

43

2

2ln16

4 i

rttr D

K

B

cR

R

GGPP

eunit volumi

2eunit volum

62

2

23 1

2ln1024

RDK

B

cGGPP i

rttr

radar constant radar reflectivity factor z, purely a property of the observed precipitation


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Radar Reflectivity Factor z

2rz PCR

To measure the reflectivity by weather radars, we need to:

- precisely know the radar constant C (radar calibration),

- measure the mean received power Pr,

- measure the range R,

- and apply the radar equation for weather radars:

Summary:

Radar observations of the atmosphere mainly contain contributions from hydrometeors which are Rayleigh scatterers at radar frequencies.

This allowed us to introduce the radar reflectivity factor z, a parameter that

- only depends on the hydrometeor microphysics and is independent on radar parameters such as the radar frequency,

- i.e. the reflectivity within the same radar resolution volume measured by different radars should be equal


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Summary of the assumptions made so far

In the derivation of the radar equation for weather radars, the following

assumptions are implied:

• the hydrometeors are homogeneously distributed within the range-bin

• the hydrometeors are dielectric spheres made up of the same material with diameters small compared to the radar wavelength

• multiple scattering among the hydrometeors is negligible

• incoherent scattering (hydrometeors exhibit random motion)

• the main-lobe of the radar antenna beam pattern can be approximatedby a Gaussian function

• far-field of the radar antenna, using linear polarisation

• so far, we neglected the propagation term (attenuation)


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Radar Meteorology




Meteorology:


Radar Meteorology:



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Radar Reflectivity Factor z

dBZm/mm1

log103610

zZ

3

6

eunit volum

6

m

mmiDz

spans over a large range; to compress it into a smaller range of numbers, a logarithmic scale is preferred

1 m3

one raindropD = 1mm

equivalent to 1mm6m-3 = 0 dBZ

raindrop diameter #/m3 Z water volumeper cubic meter

1 mm 4096 36 dBZ 2144.6 mm3

4 mm 1 36 dBZ 33.5 mm3

Knowing the reflectivity alone does not help too much.It is also important to know the drop size distribution.


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Raindrop-Size Distribution N(D)

!6)(70

0

6

eunit volum

6

N

dDDNDDz i

where N(D) is the raindrop-size distribution that tells us how many drops of each diameter D are contained in a unit volume, i.e. 1m3.

Often, the raindrop-size distribution is assumed to be exponential:

DNDN exp0

concentration (m-3mm-1) slope parameter (mm-1)

Marshall and Palmer (1948):

N0 = 8000 m-3mm-1

Λ = 4.1·R-0.21

with the rainfall rate R (mm/h)


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Reflectivity – Rainfall Rate Relations

D

dDDNDz )(6reflectivity (mm6m-3)

D

dDDND )(6

LWC 3liquid water content (mm3m-3)

D

dDDNDvDR )()(6

3rainfall rate (mm h-1)

the reflectivity measured by weather radars can be related to the liquid water content as well as to the rainfall rate:

power-law relationship

the coefficients a and b vary due to changes in the raindrop-size distribution or in the terminal fall velocity.

Often used as a first approximation is a = 200 and b = 1.6

terminal fall velocity

baRz

raindrop volume


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Summing-up

- electromagnetic waves and their interaction with precipitation

- radar principle

- radar equation for a point target

- extension of this radar equation to be applicable for volume targets and for weather radars

- the reflectivity was introduced, how it is determined from weather radar measurements, and its relation to rainfall rate (Z-R relations)

But, so far we only considered the backscattered received powerwhich is related to the amplitude of an electromagnetic wave,

what about frequency, phase and polarisation?

… more after a short break …


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2nd Part - Outline

radar geometry and displays

Doppler effect

polarisation in weather radars


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2nd Part - Outline


Doppler effect



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Radar Display

Data: POLDIRAD (DLR, Oberpfaffenhofen, Germany), Prof. Madhu Chandra

PPI (plan-position indicator):

RHI (range-height indicator):


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2nd Part - Outline


Doppler effect



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Doppler Effect

http://en.wikipedia.org/wiki/File:Dopplerfrequenz.gif

target r

d

vf

2

fd .. frequency shift caused by the moving target

vr .. relative radial velocity of the target with respect to the radar

λ .. radar wavelength

Ts .. sweep time

sr Tv

4max,


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Weather Radar Measurement Example (PPI)

Data: IDRA (TU Delft), Jordi Figueras i Ventura

Reflectivity (dBZ) Doppler velocity (ms-1)


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Combining Reflectivity and Doppler Velocity

Doppler Velocity

Power

Mean Doppler Velocity

Doppler Width

Figures: Christine Unal

Doppler Processing (Power Spectrum):

Mapping the backscattered power of one radar resolution volume into the Doppler velocity domain.


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2nd Part - Outline


Doppler effect



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Can Polarimetry add Information

yes, because hydrometeors are not spheres

- ice particles

- hail

- raindrops

Beard, K.V. and C. Chuang: A New Model for the Equilibrium Shape of Raindrops, Journal of the Atmospheric Sciences, vol. 44, pp. 1509 – 1524, June 1987. http://commons.wikimedia.org/wiki/Category:Hail


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Measurement Principle

Zhh (dBZ)

Zvh (dBZ)

Zhv (dBZ)

Zvv (dBZ)


transmit

rece

ive


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Zhh (dBZ)

Zvh (dBZ)

Zhv (dBZ)

Zvv (dBZ)


transmit

rece

ive

-

= Zdrdifferentialreflectivity


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Hydrometeor Classification

dBZlog10 2hhhh PCRZ dBlog10

vv

hhdr P

PZ

Differential ReflectivityReflectivity


rainmelting layeraggregates (snow)ice crystals


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Zhh (dBZ)

Zvh (dBZ)

Zhv (dBZ)

Zvv (dBZ)


transmit

rece

ive

-

= LDR (dB)linear depolar-

isation ratio


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Linear Depolarisation Ratio

dBZlog10 2hhhh PCRZ dBlog10

vv

hv

P

PLDR

Linear Depolarisation RatioReflectivity


melting layerground clutter


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Estimation of raindrop-size distribution

DNDN exp0

concentration (m-3mm-1) slope parameter (mm-1)

1. the differential reflectivity Zdr depends only on the slope parameter Λ,so Λ can be directly estimated from Zdr

2. once that the slope parameter is known, the concentration N0 can be estimated in a second step from the reflectivity Zhh

Data: IDRA (TU Delft), Jordi Figueras i Ventura


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Summing-up

- Doppler capabilities allow an insight into the dynamics and turbulence of precipitation

- Polarisation can be successfully applied for weather observation because hydrometeors are not spherical, main applications are:

- discrimination of different hydrometeor types,

- suppression of unwanted radar echoes, i.e. clutter,

- improving rainfall rate estimation,

- estimation of raindrop-size distribution,

- attenuation correction,

- …


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e-mail [email protected]

web http://atmos.weblog.tudelft.nlhttp://rse.ewi.tudelft.nlhttp://radar.ewi.tudelft.nl (for information on PARSAX)

references R. E. Rinehart, “Radar for Meteorologists”,Rinehart Publications, 5th edition, 2010.

R. J. Doviak and D. S. Zrnić, “Doppler Radar and Weather Observations”, Academic Press, 2nd edition, 1993.

V. N. Bringi and V. Chandrasekar, “Polarimetric Doppler Weather Radar: Principles and Applications”, Cambridge University Press, 1st edition, 2001.

A short course on radar meteorology

Tobias Otto

Documents

Remote Sensing of the Environment (RSE) ATMOS ATMOS Delft University of Technology Tobias Otto: A short course on radar meteorology.1 A short course on